In [1]:

    

# %matplotlib qt
import numpy as np
from scipy.stats import norm
import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.rc_file('matplotlibrc')
from matplotlib.cm import magma
from histogram.histogram import Histogram1D


    

    




/home/alispach/.anaconda3/envs/digicampipe/lib/python3.5/site-packages/matplotlib/__init__.py:908: MatplotlibDeprecationWarning: The backend.qt5 rcParam was deprecated in version 2.2.  In order to force the use of a specific Qt binding, either import that binding first, or set the QT_API environment variable.
  mplDeprecation)
/home/alispach/.anaconda3/envs/digicampipe/lib/python3.5/site-packages/matplotlib/__init__.py:908: MatplotlibDeprecationWarning: The backend.qt5 rcParam was deprecated in version 2.2.  In order to force the use of a specific Qt binding, either import that binding first, or set the QT_API environment variable.
  mplDeprecation)
/home/alispach/.anaconda3/envs/digicampipe/lib/python3.5/site-packages/matplotlib/__init__.py:908: MatplotlibDeprecationWarning: The backend.qt5 rcParam was deprecated in version 2.2.  In order to force the use of a specific Qt binding, either import that binding first, or set the QT_API environment variable.
  mplDeprecation)
/home/alispach/.anaconda3/envs/digicampipe/lib/python3.5/site-packages/matplotlib/__init__.py:908: MatplotlibDeprecationWarning: The backend.qt5 rcParam was deprecated in version 2.2.  In order to force the use of a specific Qt binding, either import that binding first, or set the QT_API environment variable.
  mplDeprecation)

In [2]:

    

from digicampipe.io.event_stream import event_stream
from digicampipe.calib.camera.r0 import fill_trigger_input_7, fill_trigger_patch, fill_digicam_baseline, fill_trigger_output_patch_7
from digicampipe.calib.camera.r0 import compute_trigger_patch, compute_trigger_output_7, compute_trigger_input_7
files = '/home/alispach/Downloads/SST1M_01_20180601_2954.fits.fz'

data_stream = event_stream(files, baseline_new=True)
data_stream = fill_digicam_baseline(data_stream)

n_events = 8814


    

    




/home/alispach/.anaconda3/envs/digicampipe/lib/python3.5/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  from ._conv import register_converters as _register_converters

In [3]:

    

baseline = np.array((n_events, 1296))
histo_wrong_bin = np.zeros(50)
histo_wrong_patch = np.zeros(432)
for event in data_stream:
    
    for tel_id, data in event.r0.tel.items():
    
        baseline = data.baseline
        adc_samples = data.adc_samples
        trigger_patch = data.trigger_input_traces
        trigger_input_7 = compute_trigger_input_7(trigger_patch)
        trigger_output = data.trigger_output_patch7
        '''
        patch_triggered = trigger_output.sum(axis=1) > 0
        patch_triggered = np.where(patch_triggered)[0][0]
        print(patch_triggered)
        
        plt.figure()
        plt.title('trigger patch input')
        plt.plot(trigger_patch[patch_triggered], label='online')
        plt.plot(compute_trigger_patch(adc_samples, baseline)[patch_triggered], label='offline')
        plt.legend()
        
              
        plt.figure()
        plt.title('trigger cluster input')
        plt.plot(trigger_input_7[patch_triggered], label='offline')
        plt.legend()
        plt.show()
        
        plt.figure()
        plt.title('trigger output')
        plt.plot(trigger_output[patch_triggered], label='online')
        plt.plot(compute_trigger_output_7(trigger_input_7, 58)[patch_triggered], label='offline')
        plt.legend()
        plt.show()
        '''
        
        trigger_bin = 6
        
        diff_input = trigger_patch == compute_trigger_patch(adc_samples, baseline)
        
        # diff_input = np.sum(diff_input, axis=-1)

        histo_wrong_bin += np.sum(~diff_input, axis=0)
        histo_wrong_patch += np.sum(~diff_input, axis=1)


        diff_input = diff_input[:, trigger_bin]
        where_false = np.where(~diff_input)[0]
        

        for patch_id in where_false:

            plt.figure()
            plt.title('trigger patch input {}'.format(patch_id))
            plt.plot(trigger_patch[patch_id], label='online')
            plt.plot(compute_trigger_patch(adc_samples, baseline)[patch_id], label='offline')
            plt.legend()

        assert diff_input.all()


    

In [4]:

    

plt.plot(histo_wrong_bin / 432 / n_events)
plt.figure()
plt.plot(histo_wrong_patch)


    

    
Out[4]:





[<matplotlib.lines.Line2D at 0x7fa54dbdf780>]






    




/home/alispach/.anaconda3/envs/digicampipe/lib/python3.5/site-packages/matplotlib/figure.py:2267: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  warnings.warn("This figure includes Axes that are not compatible "






    













    

In [ ]:

    

def plot_histo(data, xlabel, show_fit=True, limits=None, **kwargs):

    mask = np.isfinite(data)
    
    if limits is not None:
        
        mask *= (data <= limits[1]) * (data >= limits[0])
    
    data = data[mask]
    mean = np.mean(data)
    std = np.std(data)
    
    try:
        
        data = data[~data.mask]
    
    except:
        
        pass
    
    n_entries = len(data)
    
    label='$N_{pixels}$ = ' + '{}\n'.format(n_entries)    
    label_fit= 'Mean : {:.2f}\n'.format(mean) + 'Std : {:.2f}'.format(std)
    
    if not show_fit:
        
        label += label_fit
    
    plt.figure(figsize=(10, 10))
    hist = plt.hist(data, **kwargs, label=label)
    
    if show_fit:
        
        bins = hist[1]
        
        bin_width = bins[1] - bins[0]        
        x = np.linspace(np.min(data), np.max(data), num=len(data)*10)
        y = n_entries * norm.pdf(x, loc=mean, scale=std) * bin_width
        plt.plot(x, y, color='r', label=label_fit)

    plt.xlabel(xlabel)
    plt.ylabel('count')
    plt.legend(loc='best')


    

In [ ]:

    

from digicampipe.visualization import CameraDisplay
from ctapipe.instrument import CameraGeometry
from cts_core.camera import Camera
from digicampipe.utils.geometry import generate_geometry_from_camera
import matplotlib.pyplot as plt

def plot_camera_display(data, label, limits=None, **kwargs): 
    plt.figure()
    mask = np.isfinite(data)
    data = np.ma.masked_array(data, mask=~mask)
    cam = Camera('digicampipe/tests/resources/camera_config.cfg')
    geom = generate_geometry_from_camera(cam)
    cam_display = CameraDisplay(geom, **kwargs)
    cam_display.image = data
    cam_display.axes.set_title('')
    cam_display.axes.set_xticks([])
    cam_display.axes.set_yticks([])
    cam_display.axes.set_xlabel('')
    cam_display.axes.set_ylabel('')
    cam_display.cmap.set_bad('k')
    
    
    cam_display.axes.axis('off')
    cam_display.add_colorbar(label=label)
    cam_display.axes.get_figure().set_size_inches((10, 10))
    plt.axis('equal')
    if limits is not None:
        
        if not isinstance(limits, tuple):
            
            raise TypeError('Limits must be a tuple()')
            
        cam_display.colorbar.set_clim(vmin=limits[0], vmax=limits[1])

    
    cam_display.update()        

    return cam_display


    

In [ ]:

    

from iminuit import Minuit
from probfit import Chi2Regression


def plot_calibration_ac_led(ac_levels, charge, gain, pixel=0, crosstalk=0.08, show_fit=False):
    
    
    photoelectron = charge[pixel]/gain[pixel] * (1 - crosstalk)
    
    mask = (photoelectron > 1) * (photoelectron < 300)
    
    x = ac_levels[mask]
    y = photoelectron[mask]
    
    func = lambda x, a, b: a * x**3 + b
    
    chi2 = Chi2Regression(func, x, y)
    
    m = Minuit(chi2)
    m.migrad()
       
    #coeff = np.polyfit(x, y, deg=4)
    
    coeff = [m.values['a'], 0, 0, 0, m.values['b']]
    x_fit = np.linspace(0, 1000, num=10000)
    y_fit = func(x_fit, **m.values)
    
    # y_fit = np.polyval(coeff, x_fit)
    
    diff = np.diff(y_fit)
    diff = np.append(diff, 0)
    
    mask = (y_fit > 1) * (y_fit < 2000) * (diff > 0)
    
    x_fit = x_fit[mask]
    y_fit = y_fit[mask]
    
    fig = plt.figure(figsize=(10, 10))
    axis = fig.add_subplot(111)
    axis.errorbar(ac_levels, photoelectron, label='AC LED {}'.format(pixel), marker='o', linestyle='None', color='k')
    
    if show_fit:
        axis.plot(x_fit, y_fit, 
                  label='f(x) = {:.2f}x⁴ + {:.2f}x³ + {:.2f}x² + {:.2f}x + {:.2f}'.format(coeff[0], coeff[1], coeff[2], coeff[3], coeff[4]), color='r')
    axis.set_ylim(1, np.max(photoelectron))
    plt.xlabel('DAC')
    plt.ylabel('$N_{p.e.}$')
    axis.set_yscale('log')
    plt.legend(loc='best')


    

In [ ]:

    

def compute_transfer_function(charge, amplitude):
    
    n_pixels = len(charge)
    
    transfer = np.zeros(n_pixels)
    
    for pixel in range(n_pixels):
        
        x = charge[pixel]
        y = amplitude[pixel]
        mask = (y < 3000) * (y > 20)
        
        coeff = np.polyfit(x[mask], y[mask], deg=1)
        
        transfer[pixel] = coeff[0]
    
    transfer[transfer < 0] = np.nan
    transfer[transfer > 1] = np.nan
    
    return transfer


    

In [ ]:

    

def plot_transfer_function(charge, amplitude, pixel):
    
    x = charge[pixel]
    y = amplitude[pixel]
    
    mask = (y < 3000) * (y > 20)
    
    coeff = np.polyfit(x[mask], y[mask], deg=1)
    
    x_fit = np.linspace(np.min(x), np.max(x[mask]), num=len(x)*10)
    y_fit = np.polyval(coeff, x_fit)
        
    plt.figure(figsize=(10, 10))
    plt.errorbar(x, y, label='Pixel {}'.format(pixel), marker='o', linestyle='None', color='k')
    plt.plot(x_fit, y_fit, color='r') #, label='f(x) = {:.02f} x + {:.02f}'.format(coeff[0], coeff[1]))
    plt.xlabel('charge [LSB $\cdot$ ns]')
    plt.ylabel('amplitude [LSB]')
    plt.legend(loc='best')


    

In [ ]:

    

def compute_amplitude_baseline(charge, amplitude):

    n_pixels = len(charge)    
    baseline = np.zeros(n_pixels)
    
    for pixel in range(n_pixels):
        
        x = charge[pixel]
        y = amplitude[pixel]
        mask = (y < 3000) * (y > 20)
        
        coeff = np.polyfit(x[mask], y[mask], deg=1)
        
        baseline[pixel] = coeff[1]
        
    return baseline


    

In [ ]:

    

def mask_outliers(data, n=3):
    
    mask = np.abs(data - np.mean(data)) < (n * np.std(data))
    
    return np.ma.masked_array(data, mask=~mask)


    

In [ ]:

    

a = np.load('fmpe/fmpe_results.npz')
gain = a['gain']
baseline = a['baseline']
sigma_e = a['sigma_e']
sigma_s = a['sigma_s']
chi_2 = a['chi_2']
ndf = a['ndf']

gain_error = a['gain_error']
baseline_error = a['baseline_error']
sigma_e_error = a['sigma_e_error']
sigma_s_error = a['sigma_s_error']

b = np.load('ac_scan_run/mpe_results.npz')
amplitude = b['amplitude']
charge = b['charge']
ac_levels = b['ac_levels']
time = b['time']

c = np.load('output/dark_count_rate.npz')
dark_count_rate = c['dcr']

T = np.array([22.952428317761687, 23.26220755201969, 23.106668502533754, 22.200710364609403, 22.106867389032296, 22.69752611766469, 22.689570571292236, 22.909890498382442, 22.137065993629776, 22.22847359786838, 22.74152515984704, 23.085237234754896, 22.90501975570543, 22.81718402942997, 22.219706261049755, 22.270361984890684, 22.7908820189741, 22.30802906159292, 22.676906640332007, 23.275683273426093, 22.38677273487129, 22.26873840399835, 22.85972184880921, 22.51178846358128, 22.626413274580308, 22.65092934605461, 22.105568524318425, 22.669275810138014, 23.7297988490129, 23.005194696762654, 23.391769307228223, 22.111251057441606, 22.236753860419295, 22.96152037075878, 23.238340912902327, 23.22242982015742, 23.174858900011927, 22.258347486287388, 22.011563190652087, 23.399562495511443, 22.891868750477492, 22.12635035974035, 23.11705942024471, 22.68388803816906, 23.01363731740281, 22.612612836995442, 22.29081910413414, 22.734543762009988, 23.292893230884864, 22.609852749478467, 22.30640548070058, 22.805169530826674, 22.83439398688875, 23.11705942024471, 22.99805094083637, 21.977792708091464, 21.96123218298962, 21.897912528188456, 21.439413284192334, 21.474969705734527, 21.316670568731617, 21.640087882485254, 22.424602169662755, 23.43820372074908, 23.01802098581212, 23.365792012950823, 22.134468264202035, 22.250879014182633, 22.938140805909118, 23.466129312097287, 22.684050396258293, 22.87173634741251, 22.441000336675366, 22.28188940922628, 23.885175540409595, 23.37991716671416, 22.566827855831523, 22.094203458072066, 21.24458357711183, 20.821640754657903, 20.940324517887777, 20.98058932401775, 21.681651553329097, 22.88147783276653, 22.460970381651116, 22.768476602659845, 22.589882704502717, 22.304944257897475, 22.840076520011927, 23.40069900213608, 22.562606545511443, 22.38206435028351, 22.918657835201067, 22.422816230681182, 22.748344199594857, 22.85095451199059, 22.176031935045874, 22.80516953082667, 22.717333804551213, 22.32199185726702, 22.34407255740281, 22.040787646714158, 20.908015258130263, 20.878790802068185, 21.808615579109894, 21.27526925597701, 21.588133293930454, 21.333555810011923, 21.59073102335819, 22.456586713241805, 23.71940793130194, 22.99886273128254, 23.237691480545394, 22.178954380652083, 22.252177878896504, 22.772860271069153, 23.00275932542415, 23.1251773247064, 23.062344744172936, 22.295365130632682, 22.21629674117585, 23.659010722106984, 23.410278129400876, 23.429761100108923, 22.957136702349466, 22.020330527470705, 21.775819245084676, 22.976132598789814, 22.269063120176817, 21.244908293290298, 21.377554852194272, 20.765951930050726, 20.896812549973134, 20.947955348081763, 21.1544748375871, 21.82988448879951, 23.138165971845098, 22.75256550991493, 22.81328743528836, 22.370536925947917, 22.061082407868376, 22.51747099670446, 23.194341870719978, 22.28611071954636, 22.14469682382376, 22.997076792300966, 22.61683414731552, 22.884887352640444, 23.02467766747071, 22.144047391466827, 22.42054321743191, 22.93635486692754, 22.78714778292173, 22.976457314968282, 22.67853022122434, 21.905705716471676, 22.04955498353278, 21.72548823742221, 21.176230821544422, 20.790143285346556, 20.20987547442512, 20.356160112824735, 20.614634190884864, 22.232694908188456, 21.625475654454213, 22.042735943784965, 21.622390850758777, 21.790756189294182, 22.596864102339765, 23.399887211689915, 22.79591511974035, 23.07582046557934, 21.815272260768477, 21.8759941861419, 22.5705620918839, 23.32406598401775, 22.97726910541445, 22.959734431777207, 22.351541029507562, 22.22246634856673, 23.85367807109825, 23.555263903086615, 23.207492875947914, 22.993180198159358, 22.33108391026411, 22.219706261049755, 23.639852467577406, 23.310427904522115, 22.618782444386326, 22.127649224454217, 21.107553349798543, 20.516407546898446, 20.413797234502717, 20.317843603765567, 21.021178846326187, 21.962855763881954, 21.52741136855703, 21.73863924265014, 21.649829367839278, 21.618981330884868, 22.160770274657903, 23.010065439439664, 22.47980392000223, 22.438727323426086, 22.138364858343643, 21.85699828970155, 22.306567838789817, 23.328936726694764, 22.44035090431843, 22.284649496743256, 23.283638819798547, 22.919144909468766, 22.904857397616194, 22.8673526790032, 22.089170357305818, 22.446195795530844, 22.97337251127284, 22.634368820952766, 22.771561406355282, 22.8808284004096, 22.303970109362073, 22.58144008386256, 22.466003482417364, 22.055724590923663, 22.239189231757805, 21.9803904375192, 20.881226173406695, 20.71691978710213, 22.391318761369835, 21.4517524989741, 21.83183278587032, 21.069886273096312, 21.383237385317454, 21.745458282397966, 22.88894630487129, 22.173758921796605, 22.481589858983803, 21.66379216351338, 21.791892695918815, 22.448468808780113, 23.660634302999323, 22.543610649071095, 22.745259395899417, 22.02568834441542, 22.162069139371773, 22.603520783998352, 23.261071045395052, 22.89641477697604, 22.554326282960524, 23.84361186956576, 23.34777026504588, 23.072248587616198, 22.94122560960456, 22.32426487051629, 22.261757006161293, 23.862932482184576, 23.433657694250535, 23.107642651069153, 22.501559903959553, 21.910251742970225, 21.71931863003133, 23.065754264046845, 22.33887709854733, 21.38161380442512, 22.010426684027447, 21.721754001369835, 22.18918294027381, 21.691068322504652, 21.391030573600677, 21.73052133818846, 22.51698392243676, 22.051990354871286, 22.19843735136013, 21.975844411020656, 21.639113733949852, 22.152977086374683, 23.309129039808244, 22.631771091525025, 22.43970147196149, 22.024876553969253, 21.97259724923598, 22.3911564032806, 23.35393987243676, 22.78178996597701, 22.816696955162264, 22.545071871874196, 22.419244352718035, 22.63972663789748, 22.940900893426086, 22.13804014216518, 22.532083224735498, 23.159921955802425, 22.799324639614255, 22.918820193290298, 22.46681527286353, 21.806180207771387, 22.177655515938213, 22.04598310556964, 21.353038780719974, 20.95120250986644, 20.95298844884801, 21.29605109139893, 21.91999322832425, 23.322929477393114, 22.240163380293215, 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charge = charge - baseline[:, np.newaxis]
baseline_amplitude = compute_amplitude_baseline(charge, amplitude)
amplitude = amplitude - baseline_amplitude[:, np.newaxis]
transfer = compute_transfer_function(charge, amplitude)
gain_amplitude = gain * transfer
sigma_e_amplitude = sigma_e * transfer
sigma_s_amplitude = sigma_s * transfer

from digicampipe.utils import Camera
cam = Camera('digicampipe/tests/resources/camera_config.cfg')
geom = cam.geometry

photoelectrons = charge / gain[:, None]

x = geom.pix_x
y = geom.pix_y
pixel_id = geom.pix_id

x = x[pixel_id]
y = y[pixel_id]

r = np.sqrt(x**2 + y**2)


    

In [ ]:

    

print(photoelectrons.shape)
plt.semilogy(ac_levels, photoelectrons.T)


    

In [ ]:

    

gain = mask_outliers(gain, n=2)


    

In [ ]:

    

print(gain.mask.shape)
print(T[~gain.mask].shape)
plot_histo(gain, 'Gain [LSB $\cdot$ ns]', bins='auto', show_fit=True)
plot_histo(gain, 'Gain [LSB $\cdot$ ns]', bins='auto', show_fit=False)
plot_camera_display(gain, 'Gain [LSB $\cdot$ ns]')
plot_correlation(gain[~gain.mask], T[~gain.mask], T[~gain.mask], label_x='Gain [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

sigma_e = mask_outliers(sigma_e, n=2)


    

In [ ]:

    

plot_histo(sigma_e, '$\sigma_e$ [LSB $\cdot$ ns]', bins='auto', show_fit=True)
plot_histo(sigma_e, '$\sigma_e$ [LSB $\cdot$ ns]', bins='auto', show_fit=False)
plot_camera_display(sigma_e, '$\sigma_e$ [LSB $\cdot$ ns]')
plot_correlation(sigma_e[~sigma_e.mask], T[~sigma_e.mask], T[~sigma_e.mask], label_x='$\sigma_e$ [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

sigma_s = mask_outliers(sigma_s, n=2)


    

In [ ]:

    

plot_histo(sigma_s, '$\sigma_s$ [LSB $\cdot$ ns]', bins='auto', show_fit=True)
plot_histo(sigma_s, '$\sigma_s$ [LSB $\cdot$ ns]', bins='auto', show_fit=False)
plot_camera_display(sigma_s, '$\sigma_s$ [LSB $\cdot$ ns]')
plot_correlation(sigma_s[~sigma_s.mask], T[~sigma_s.mask], T[~sigma_s.mask], label_x='$\sigma_s$ [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

baseline = mask_outliers(baseline, n=2)


    

In [ ]:

    

plot_histo(baseline, 'Baseline [LSB $\cdot$ ns]', bins='auto', show_fit=True)
plot_histo(baseline, 'Baseline [LSB $\cdot$ ns]', bins='auto', show_fit=False)
plot_camera_display(baseline, 'Baseline [LSB $\cdot$ ns]')
plot_correlation(baseline[~baseline.mask], T[~baseline.mask], T[~baseline.mask], label_x='Baseline [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    




    

In [ ]:

    

plot_calibration_ac_led(ac_levels, charge, gain, pixel=100, show_fit=False)


    

In [ ]:

    

plot_transfer_function(charge, amplitude, 100)


    

In [ ]:

    

plot_camera_display(transfer, label='amplitude / charge')
plot_histo(transfer, xlabel='amplitdude / charge', bins='auto')


    

In [ ]:

    

plot_camera_display(gain_amplitude, label='Gain [LSB]')
plot_histo(gain_amplitude, xlabel='Gain [LSB]', bins='auto')


    

In [ ]:

    

plot_histo(dark_count_rate * 1E3, 'DCR [MHz]', bins='auto', show_fit=False, limits=(0, 15))
plot_camera_display(dark_count_rate * 1E3, label='DCR [MHz]', cmap=magma, limits=(0, 15))
plot_correlation(dark_count_rate*1E3, T, T, label_x='DCR [MHz]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

plot_camera_display(sigma_e_amplitude, '$\sigma_e$ [LSB]', limits=(0, 1))


    

In [ ]:

    

plot_correlation(gain, T, T, label_x='Gain [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

plot_correlation(gain, sigma_e, T, label_x='Gain [LSB $\cdot$ ns]', label_y='$\sigma_e$ [LSB $\cdot$ ns]', cmap=magma)


    

In [ ]:

    

plot_correlation(sigma_e, T, T, label_x='$\sigma_e$ [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

plot_correlation(sigma_s, T, T, label_x='$\sigma_s$ [LSB $\cdot$ ns]', label_y='T [°C]', cmap=magma)


    

In [ ]:

    

plot_correlation(r, sigma_s, T, label_x='r [mm]', label_y='$\sigma_s$ [LSB $\cdot$ ns]', label_c='T [°C]', cmap=magma)


    

In [ ]:

    

plot_correlation(r, T, T, label_x='r [mm]', label_y='T [°C]', label_c='T [°C]', cmap=magma)


    

In [ ]:

    

plot_correlation(y, T, T, label_x='y [mm]', label_y='T [°C]', label_c='T [°C]', cmap=magma)


    

In [ ]:

    

plot_camera_display(T, label='T [°C]', cmap=magma)
plot_histo(T, 'T [°C]', outliers=True, show_fit=True, bins='auto')


    

In [ ]:

    

print(dark_count_rate.tolist())
print(sigma_e_amplitude.tolist())
print(sigma_s_amplitude.tolist())
print(gain_amplitude.tolist())
print(len(gain_amplitude.tolist()))